And while a detailed search has yet to take place – with police unable to enter the building – they have said they do not believe there are any more people unaccounted for.
Meanwhile, residents of nearby flats have started to return home, after being evacuated after the explosion and fire.
Today (Thursday, July 7) searches of the outer cordon were completed and residents were able to return to 78 flats in the adjacent block.
However, a large part of the affected building remains unsafe and it will be some time before full examination and investigations can be carried out.
Last night (Wednesday) police worked with structural engineers, fire investigators from Bedfordshire Fire and Rescue Service and specialist teams to recover the body of the one person who is known to have died in the incident.
A post mortem is due to be held tomorrow (Friday).
While formal identification is yet to take place, officers are supporting the believed next of kin.
Chief Superintendent John Murphy, from Bedfordshire Police, said: “This remains an incredibly complex investigation which will take some time to carry out.
“However, we’ve been working hard to get as many residents back into their homes as possible and I’d like to thank everyone who has been impacted for their patience and understanding at this difficult time.
“While we cannot currently physically enter the building to carry out a proper search, based on our investigations so far, and the information we have received, we do not believe there is anybody else unaccounted for, either as residents or visitors.
“It is a tragedy that one person has lost their life and our thoughts are very much with their loved ones.
“However, it’s welcome that we can be cautiously optimistic that there will be no further victims.”
Floral tributes left for the victim were also moved closer to the flats now the wider cordon has been removed.
In addition to the significantly damaged flats, six further neighbouring flats remain unsafe to return to, but it is hoped that residents will be able to briefly access their homes in the coming weeks, after they have been made structurally safe, to retrieve important and sentimental items.
Forensic teams assisted by Bedfordshire Fire and Rescue Service are continuing investigations including CCTV enquiries as they seek to establish the cause of the explosion.
It has been confirmed there is no mains gas supply into the building.
An information centre has been set up for people to get in touch, report any concerns or find out about family members.
Concerned family and friends can also call 0800 051 6085.